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Log, a log. p sin 'log. A ; log. ulog. p cos + log. sin H;
log. flog. p sin p' + log. cos D', log. Glog. p cos p' + log. cos H,
log. vlog. ulog. sin D'+9.4180; log. g = log. G+ log. sin D'
3. With the values of p, q, u, v, &c., found for the requisite times, make the computation by Arts. 8, 9, &c., of the rule to Prob. XVI., using logarithms to four decimal figures, and natural numbers to three or four decimals. Then, for the times of beginning and end thus found, taken to the nearest hundredth of an hour, repeat the calculation, using logarithms to five or more decimal figures.
When the eclipse is annular or total, the times of its beginning and ceasing to be so, are found in a similar manner, only using 7 instead of 1.
Note.-The general quantities, whose values are found by the first article, serve not only for calculating the times of beginning, &c., of an clipse for any place at which it will be visible, but also for the calculations requisite to determine the longitude of a place, from the observed times of beginning and end at that place.*
Let it be required to compute, for Philadelphia, the eclipse of May 15th, 1836.
1. For quantities independent of the place.
By the Nautical Almanac, the time of new moon is May 15th, at 2hrs. 6.9m. Taking, therefore, T 15d. 2h., we find from the Nautical Almanac,† and from tables of sines, tangents, &c., the following quantities :
15 051° 10′ 25′′.35 52° 15′28′′.95
10′25′′.358 52°15′28′′.9565 3.6054′25′′.60
3729 .00 54 24 .90
54' 17".12 54 16 .42
151 40 28 .1452 17 57 .14 252 10 33 .90 52 20 25 .34 9 51 .44 54 24 .218.48 54 15 .73 352 40 42 .6252 22 53 .55 17 49 .0754 23 .53 453 10 54 .30 52 25 21 .78+45 32 .52 54 22 .85
54 15 .05 54 14 .73
*The values of p, q, u, v, &c., are found by the formulæ in Art. 75 of the Appendix. To find them by the formulæ in (App. 69), the values of a, d, and g, must first be computed (App. 68). For all important eclipses, these and the other general data are given in the Berlin Ephemeris.
†The values of A, A′, D, D', 7, and f' may be obtained from the part of the Nautical Almanac given in Table LXV. The value of is given in a different x part of the Almanac.
18°56′ 35.90′′N. + 4'48.80" 15′ 49.90" 7.6632559
23 49.82 15 49.88 7.6632491 +33 12.54 15 49.88 7.6632456 +42 30.07 15 49.87 |7.6632422
Making similar calculations for the other hours, finding the values of p and q for the half hours, by the last problem, and proceeding as directed in the rule, we obtain the following values.
Making now the approximate calculation, the results obtained would be nearly the same as those found in the first example to Prob. XVI. We may, therefore, for finding the times of beginning and end more accurately, take T′ = 0.06h. for the beginning, and T' = 2.56h. for the end.
p=-1.10417;q=0.10258; p=0.4807; d=0.1738; H-73°17′0′′.
h = 1 − (a + b) =.56290
log. G. 9.3440 log. B. 7.6391
Beginning 7 3 23.5 A. M., Philad'a mean time.
If a more accurate computation of the time of greatest obscuration and of the quantity of the eclipse is desired, let T' the time before found, taken to the nearest hundredth of an hour, and find the values of p, q, u, v, &c., for this time. The computation may then be made by articles 8 and 10 of the rule to Prob. XVI., using logarithms to five decimal figures, and putting the value of g' found by the first part of the present rule, in stead of the number 2732.